I assume you mean exchanging your coins to fiat, correct?
I can't answer how to exchange your coins quickly and cheaply as possible, but I can answer other question.
Is it possible to withdraw and convert to fiat quickly without creating an account, verification procedures? Is there something like that now? What does it look like at this moment?
I know that there are many such topics, but I think it is worth to refresh the topic a little because a lot has changed recently.
Exchanges do require account in order to trade, I believe there are no true anonymous exchange that lets you do it without an account yet.
Exchanges requires verification in order to withdraw your fiat, this, I believe is to prevent any possible money laundering or other related shady activities.
Verification are almost the same between exchanges, you need to submit your Identity Proof and Bank Statement, others may require more than that, but usually you only need those two.
P.S. Wrong section, might want to move this to trading discussion or exchanges section